Optimization design method of skin conformal antenna under fatigue reliability constraint

Abstract

The invention discloses an optimization design method of a skin conformal antenna under fatigue reliability constraint. The method comprises the following steps: firstly, analyzing a skin conformal antenna structure and a service load thereof, identifying a main failure mode of the skin conformal antenna structure, representing and quantifying multi-source uncertainty such as a service environment, a composite material layering structure and material performance, establishing a performance simulation analysis model under multi-physics field coupling, and simulating performance response of the model under the action of multi-physics field coupling; the method comprises the following steps: firstly, simulating a skin conformal antenna, then, constructing a performance prediction model based on deep learning on the basis of a simulation result, then, establishing a skin conformal antenna integrated optimization design model under fatigue reliability constraint, finally, solving an optimal design variable by utilizing an intelligent optimization algorithm, and carrying out multi-physics field performance analysis on an optimized structure to verify an optimization effect. According to the method, key technical support is provided for aircraft design optimization and collaborative design of an electromagnetic and structural system, and reliable operation and high performance of the aircraft under complex working conditions can be ensured.

Description

Technical Field

[0001] This invention belongs to the field of integrated wing antenna technology, specifically relating to an optimization design method for a conformal skin antenna under fatigue reliability constraints. Background Technology

[0002] With the continuous development of aerospace technology, composite materials have many advantages such as high specific strength, high specific modulus, and strong designability. They can effectively reduce the weight of aircraft, improve fuel efficiency and flight performance, and are increasingly widely used in wing structures. However, composite material wings are subjected to a variety of complex loads during flight, such as aerodynamic loads, inertial loads, and engine vibrations, which result in complex dynamic behaviors, including deformation, vibration, and changes in natural frequency.

[0003] Conformal antennas with skin are structures that integrate antenna functionality with the aircraft skin, possessing excellent aerodynamic shape and stealth characteristics, and are widely used in the aerospace field. However, in actual service, this structure faces complex mechanical loads and fatigue reliability challenges.

[0004] Current design methods typically optimize only a single discipline (such as structural strength or electromagnetic performance), failing to fully consider multi-physics coupling effects and fatigue reliability constraints. This may result in the designed antenna failing to meet lifespan and reliability requirements under actual operating conditions, thereby increasing maintenance costs and safety risks. Especially when the antenna is integrated into the surface or interior of the wing to support functions such as communication and navigation, the dynamic characteristics of the wing will significantly affect the antenna performance, mainly in the following aspects: (1) Position and attitude deviation: The deformation and vibration of the wing will change the actual installation position and orientation of the antenna, causing it to deviate from the designed operating state. For example, bending deformation may cause distortion of the antenna radiation pattern, affecting the signal coverage and reception quality. (2) Electromagnetic environment disturbance: The dynamic behavior of the wing will change the electromagnetic field distribution around the antenna, which may cause impedance mismatch and increase the reflection coefficient, thereby reducing radiation efficiency and gain. (3) Structural and antenna coupled vibration: The vibration of the wing may generate a coupled response with the antenna, which not only aggravates structural fatigue damage, but may also cause unstable fluctuations in the electrical performance of the antenna.

[0005] In actual service, conformal skin antennas operate in a highly coupled environment involving multiple physical fields such as aerodynamics, structure, heat, and electromagnetic fields, posing a severe challenge to their reliability. Currently, there is a lack of optimization design methods that address multidisciplinary reliability constraints. Therefore, developing an effective reliability design and optimization method for conformal skin antennas can provide an effective technical approach to improving the overall performance of aircraft. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides an optimization design method for conformal antennas with skin under fatigue reliability constraints. By comprehensively applying theoretical modeling and numerical calculation, the method enables performance analysis, prediction, and optimization of conformal antennas with composite material wing skins, thereby providing a scientific basis and effective means for aircraft design improvement and reliability assurance.

[0007] The technical solution adopted in this invention is: an optimization design method for a skin conformal antenna under fatigue reliability constraints, the specific steps of which are as follows:

[0008] S1. Analyze the conformal antenna structure and service load of composite material wing skin, and identify the main failure modes of the conformal antenna.

[0009] The skin antenna consists of: upper and lower composite material layers, a honeycomb structure and an antenna array; the composite material layers are made of single-layer composite materials laid up at different angles, and the structural optimization design takes into account the layup geometry of the single-layer materials to withstand aerodynamic loads, vibration and temperature loads.

[0010] The ply geometry includes: the thickness of each single layer, the ply direction, and the ply sequence.

[0011] First, a three-dimensional finite element model of the conformal antenna of the composite material wing skin is constructed based on the finite element analysis method. During the modeling process, the geometry of the wing, the layup structure of the upper and lower composite material plates, the fiber direction, the material properties and the boundary conditions are set, and the element mesh is divided according to the actual situation.

[0012] The material properties include: elastic modulus, Poisson's ratio, shear modulus, and density.

[0013] To address the anisotropic properties of composite materials, a suitable material constitutive model is employed to describe their mechanical behavior. The principal directions of the material are represented by coordinates l, 2, and 3. The expressions for stress distribution and strain in the upper and lower composite laminates within coordinate system 1, 2, and 3 are as follows:

[0014] (1);

[0015] in, , , , , , Represents stress components in tensor form. Represents the normal stress along the principal axes of the material. Represents shear stress; , , , , , Represents strain components in tensor form. Represents the normal strain along the principal axis of the material. Indicates shear strain; , This represents the elastic modulus of a composite material in the tensile direction. , , Indicates shear modulus, and It represents Poisson's ratio.

[0016] Finally, the main failure modes of the skin antenna were determined, including: 1) under multi-physics coupling, the deformation of the upper and lower composite material layers and the antenna array exceeds the allowable value; 2) under multi-physics coupling, the fatigue life of the upper and lower composite material layers is less than the design value; 3) the static strength is greater than the yield strength; 4) the antenna return loss is greater than the allowable value.

[0017] S2. Based on step S1, characterize and quantify the multi-source uncertainty factors of the skin conformal antenna, establish a performance simulation analysis model of the skin conformal antenna, and simulate its performance response under multi-physics coupling.

[0018] S21. Characterize and quantify the multi-source uncertainties of conformal skin antennas;

[0019] The multi-source uncertainty factors include: the dimensions of the conformal antenna structure, material properties, and multi-source load uncertainty.

[0020] Considering manufacturing errors, the layup thickness and honeycomb thickness of the single-layer composite material laminate are random uncertain design variables, the elastic modulus of the material mechanical properties is a random design parameter, and the inflow velocity, angle of attack, and temperature load are random uncertain parameters.

[0021] S22. Based on the random distribution characteristics of the design parameters and variables in step S21, perform Latin hypercube sampling and simulate and analyze the performance response of the conformal antenna with composite material skin under multi-physics coupling.

[0022] The performance of the composite material skin conformal antenna under multi-physics coupling includes: the stress and strain of the skin antenna, as well as the antenna's electrical performance, radiation pattern, and gain.

[0023] First, Latin hypercube sampling is performed. The dynamic analysis expression of the conformal antenna with composite skin under multiphysics coupling is as follows:

[0024] (2);

[0025] in, This represents the conformal antenna mass matrix of the wing skin. Indicates structural deformation. This represents the first derivative of the transformation. Represents the transformed second derivative; Represents the structural damping matrix. Represents the structural stiffness matrix. This indicates the load that the structure bears.

[0026] Then, the antenna type, geometry, feeding method, radiating element layout, and relative positional relationship with the skin are defined, and the antenna's electrical performance is analyzed, as shown in the following expression:

[0027] (3);

[0028] in, This indicates the electrical performance of the antenna. and Indicates spatial orientation. Indicates antenna structural parameters, Indicates temperature. , and Indicates the first time the array surface is subjected to external load and temperature load. line, number Positional deviation of each radiation unit Functions representing the effects of external loads and temperature loads. and This indicates the spacing between radiating elements, setting the antenna to have... One radiation unit; and They represent the first line, number The amplitude and phase of the excitation current of the column position radiation element; Represents the free space wave constant. Indicates the wavelength in free space; The element radiation pattern is represented by the following expression:

[0029] (4);

[0030] in, and These represent the length and width of the rectangular radiating element, respectively. This indicates the thickness of the antenna array.

[0031] Antenna electrical performance parameters include: antenna gain and return loss; antenna gain The expression is as follows:

[0032] (5);

[0033] in, Radiation efficiency refers to the proportion of input power converted into radiated power. The directivity coefficient describes the spatial concentration of energy radiated by an antenna. The expression for the directivity coefficient is as follows:

[0034] (6);

[0035] in, Indicates the antenna in direction The radiation intensity, , This represents the total radiated power of the antenna; if the far-field radiation pattern of the antenna is known... The directional coefficient is then calculated by integration, as shown in the following expression:

[0036] (7);

[0037] in, Represents the maximum directionality coefficient. Represents the solid angle of the entire sphere, and , This represents the normalized pattern function.

[0038] Return loss The expression is as follows:

[0039] (8);

[0040] in, The voltage reflection coefficient is expressed as follows:

[0041] (9);

[0042] in, This indicates the input impedance of the antenna. This represents the characteristic impedance of the transmission line.

[0043] S23. Based on the stress and strain analysis results from step S22, the fatigue life of the composite material skin structure is evaluated using the critical plane method, as shown in the following expression:

[0044] (10);

[0045] in, Indicates the range of shear strain. Indicates the range of normal strain. Indicates the structural fatigue life. Represents a constant. and These represent the fatigue strength index and the fatigue ductility index, respectively. Indicates the elastic modulus. Indicates the fatigue strength coefficient. This represents the fatigue ductility coefficient.

[0046] S3. Based on the multi-physics coupling performance analysis in step S2, establish a deep learning-based performance prediction model for the skin conformal antenna.

[0047] First, the deep learning network structure of the deep learning-based conformal antenna performance prediction model is determined. A multi-layer fully connected network is adopted, and the input nodes of the first layer are: the thickness of the upper and lower composite plates, the thickness of the upper and lower honeycomb structures, temperature, material elastic modulus, incoming flow velocity, and angle of attack. express.

[0048] in, Indicates design variables, Indicates the number of design variables. Indicates design parameters, Indicates the number of design parameters. This indicates the transpose operation.

[0049] Output layer node is , These represent the maximum stress, strain, maximum deformation, and electrical performance of the conformal antenna with skin, respectively; The output of the hidden layer nodes is , Indicates the first Hidden layer The output of each node; The activation function is expressed as follows:

[0050] (11);

[0051] Then the first Hidden layer output layer nodes The input and output calculation expressions are as follows:

[0052] (12);

[0053] in, Indicates the first The first hidden layer One neuron, Indicates the first One output, Indicates the first One input, Indicates the number of inputs. This indicates the number of nodes in each hidden layer. Indicates the first The first hidden layer The threshold of a neuron; Indicates the first Hidden layer nodes With the Hidden layer nodes Weighting coefficients; This represents the bias term for each layer of the neural network.

[0054] Get the sum of the output values ​​of all output layers Then compare it with the corresponding true value Compare the errors of the obtained sample points, and then obtain the total errors of all training samples. Let the total number of errors be... For each sample point, the total error function is... The expression is as follows:

[0055] (13);

[0056] Then, gradient descent is used to correct the weights and thresholds to minimize the total error for the hidden layer. There are 1 node, and the learning rate is set to 1. The weight adjustment amount is The threshold adjustment amount is The steepest gradient descent method is used to calculate the weights of each layer, and the adjustment amount of the weights of the output layer nodes is calculated similarly. and threshold adjustment amount The expression is as follows:

[0057] (14);

[0058] in, Indicates the output layer activation value. This represents the adjustment amount of the output layer activation value. This represents the input value of the y-th node in the input layer. This represents the target output value of the j-th node in the output layer. This represents the weight between the i-th input node and the j-th hidden layer node. This represents the input value of the s-th node in the input layer.

[0059] Finally, the root mean square error (RMSE) and the coefficient of determination were used as the basis for the analysis. The performance of a machine learning model can be evaluated using the following expression:

[0060] (15);

[0061] (16);

[0062] in, Indicates the number of test samples. This represents the experimental value for each test sample. This represents the predicted value of each test sample based on the deep learning model. express The average of the test values ​​of the test samples.

[0063] S4. Based on the performance prediction model of the conformal antenna with skin established in step S3, establish an integrated optimization design model of the conformal antenna with skin under fatigue reliability constraints.

[0064] Define the optimization design variables, objective function, and constraints, and establish an integrated optimization design model for the skin conformal antenna under fatigue reliability constraints.

[0065] S5. Based on step S4, solve the optimal design variables of the skin conformal antenna using an intelligent optimization algorithm, analyze the multi-physics performance of the optimized structure, verify the optimization results, and complete the skin conformal antenna optimization design under fatigue reliability constraints.

[0066] Furthermore, step S4 is specifically as follows:

[0067] S41. Optimize the design variables, objective function, and constraint conditions;

[0068] The optimization design variables include: the layup thickness and cell thickness of the single-layer composite material plate; the objective function is to maximize the gain of the antenna array; the constraints include: fatigue reliability constraints of the skin structure, maximum mass constraints, return loss constraints, and maximum deformation constraints.

[0069] S42. Based on step S41, establish an integrated optimization design model for skin conformal antenna under fatigue reliability constraints.

[0070] The expression for the integrated optimization design model of the conformal antenna with skin is as follows:

[0071] (17);

[0072] in, Indicates antenna gain. Represents a vector of random design variables. Represents a vector of random design parameters. This indicates the required fatigue life of the wing structure. Indicates minimum return loss. This indicates the allowable return loss value. This indicates the maximum deformation of the conformal antenna structure with skin. This indicates the maximum allowable deformation of the conformal antenna structure with skin. This indicates the weight of the conformal antenna structure with skin. This indicates the maximum allowable weight of the conformal antenna structure with skin.

[0073] Furthermore, step S5 is specifically as follows:

[0074] First, based on the first-order Taylor expansion method, the fatigue reliability constraint is expanded at the mean of the random design variables and random design parameters using the first-order Taylor expansion method, as shown in the following expression:

[0075] (18);

[0076] in, and These represent the mean vectors of the design variables and design parameters, respectively. Indicates the number of design variables. Indicates design variables, Indicates the number of design parameters. Indicates design parameters, This represents the mean of the design variables. This represents the average value of the design parameters.

[0077] Then, based on the augmented Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem, as shown in the following expression:

[0078] (19);

[0079] in, Describe the objective function. Indicates the output. Indicates the first The Lagrange multipliers of the next iteration, Indicates the first The penalty factor for each iteration. Indicates the first Lagrange multipliers for each inequality constraint in each iteration Indicates the first Slack variables of a constraint, Indicates the first One constraint condition. Indicates the number of constraints.

[0080] Then minimize the slack variables to transform equation (19) into one containing only design variables. and objective function The expression is as follows:

[0081] (20);

[0082] Then, the Particle Swarm Optimization (PSO) algorithm is used to solve the unconstrained optimization design problem of equation (20), and the following is set: In a 1-dimensional space, there are Q particles; particles Represented as ,Will Substitute into the fitness function Find the fitness value; particle speed ,particle The best position an individual has ever experienced: The best position the population has ever experienced: ,particle The The dimensional velocity update expression is as follows:

[0083] (twenty one);

[0084] in, Indicates the first Sub-iteration particles The first of the flight velocity vectors dimensional components, Indicates the first Sub-iteration particles The position vector of the first dimensional components, , Represents the acceleration constant. , Let [the two numbers] represent two random functions, with values ​​ranging from [0, 1]. This represents the inertia weight.

[0085] particle The The dimension component update expression is as follows:

[0086] (twenty two);

[0087] The fatigue reliability index iteration is based on the first-order second-moment method to evaluate fatigue reliability, and the expression is as follows:

[0088] (twenty three);

[0089] in, This indicates the required fatigue life. and Let represent the mean and standard deviation of fatigue life, respectively. and This represents the vector of mean values ​​of the random design variables and random design parameters. This represents the vector of the mean and optimal values ​​of random design variables. This represents the integral function of the standard normal distribution.

[0090] Finally, the optimization results were verified and confirmed by combining simulation analysis, the optimization results of the design variables were obtained, the geometric model of the conformal antenna of the composite material wing skin was established, and the multi-physics coupling performance was analyzed based on the finite element simulation method to obtain the stress, strain and maximum deformation data of the critical section. Then, the antenna return loss and gain electrical performance were analyzed by software simulation to verify the optimization results and complete the optimization design of the conformal antenna of the skin under fatigue reliability constraints.

[0091] The beneficial effects of the present invention: The method of the present invention first analyzes the conformal antenna structure and its service load, identifies its main failure modes, then characterizes and quantifies the multi-source uncertainties such as service environment, composite material ply structure and material properties, establishes a performance simulation analysis model under multi-physics coupling, simulates its performance response under multi-physics coupling, then constructs a performance prediction model based on deep learning based on simulation results, then establishes an integrated optimization design model of conformal antenna under fatigue reliability constraints, finally uses intelligent optimization algorithm to solve the optimal design variables, and performs multi-physics performance analysis on the optimized structure to verify the optimization effect. The method of the present invention proposes a high-precision, multi-disciplinary coupled optimization design method, providing a technical approach to solve the performance stability and reliability problem of conformal antenna in complex service environment. Specifically: (1) Establishing a performance analysis model of conformal antenna of composite material wing skin under multi-physics coupling can accurately simulate and predict the dynamic behavior of the wing (such as deformation and vibration) and its actual impact on key electrical performance such as antenna radiation characteristics and impedance matching. (2) The integrated optimization design of conformal antenna with skin under fatigue reliability constraints not only optimizes the electromagnetic and structural performance of the antenna, but also ensures that it meets the predetermined fatigue life and reliability indicators under long-term aerodynamic, mechanical and thermal load coupling, providing technical support for the collaborative design and comprehensive performance improvement of the electromagnetic and structural systems of aircraft. Attached Figure Description

[0092] Figure 1 This is a flowchart of an optimization design method for a conformal antenna with skin under fatigue reliability constraints according to the present invention.

[0093] Figure 2 This is a diagram of a multilayer fully connected neural network structure in an embodiment of the present invention.

[0094] Figure 3 The diagram shows the skin conformal antenna structure and service load analysis results in an embodiment of the present invention.

[0095] Figure 4 This is a diagram showing the antenna electrical performance analysis results in an embodiment of the present invention. Detailed Implementation

[0096] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0097] like Figure 1 The flowchart shown is a method for optimizing the design of a conformal antenna with a skin under fatigue reliability constraints according to the present invention. The specific steps are as follows:

[0098] S1. Analyze the conformal antenna structure and service load of composite material wing skin, and identify the main failure modes of the conformal antenna.

[0099] This embodiment employs a composite material wing for a small unmanned aerial vehicle (UAV), with a microstrip antenna mounted on its surface for communication. The wing is made of carbon fiber reinforced composite material, featuring a specific airfoil and ply structure. The antenna is located near the leading edge of the wing and operates at a frequency of 2.4 GHz.

[0100] The skin antenna comprises: upper and lower composite material layers, a honeycomb structure, and an antenna array. The composite material layers are made by laying up single layers of composite material at different angles. The structural optimization design takes into account the layup geometry of the single layers of material and withstands aerodynamic loads, vibration loads, and temperature loads.

[0101] The ply geometry includes: the thickness of each layer, the ply direction, and the ply sequence. In this embodiment, the initial ply angle uses a [45 / -45 / -45 / 45] symmetrical laminate, and the ply material parameters are as follows: =138GPa =9GPa =0.3、 =6.9 GPa, initial layup thickness =0.25mm.

[0102] First, a three-dimensional finite element model of the conformal antenna of the composite wing skin is constructed based on the finite element analysis method. During the modeling process, the geometry of the wing, the layup structure of the upper and lower composite material plates, the fiber direction, the material properties and boundary conditions are set, and the element mesh is divided according to the actual situation to ensure that the model can accurately simulate the mechanical behavior of the wing under various loads.

[0103] The material properties include: elastic modulus, Poisson's ratio, shear modulus, and density.

[0104] Furthermore, considering the anisotropic properties of composite materials, a suitable material constitutive model is used to describe their mechanical behavior. The principal directions of the material are described using coordinates l, 2, and 3. Then, in coordinate system 1, 2, and 3, the expressions for the stress distribution and strain of the upper and lower composite material laminates are as follows:

[0105] (1);

[0106] in, , , , , , Represents stress components in tensor form. Represents the normal stress along the principal axes of the material. This represents shear stress. , , , , , Represents strain components in tensor form. Represents the normal strain along the principal axis of the material. This represents shear strain. , This represents the elastic modulus of a composite material in the tensile direction. , , Indicates shear modulus, and It represents Poisson's ratio.

[0107] Finally, the main failure modes of the skin antenna were determined, including: 1) under multi-physics coupling, the deformation of the upper and lower composite material layers and the antenna array exceeds the allowable value; 2) under multi-physics coupling, the fatigue life of the upper and lower composite material layers is less than the design value; 3) the static strength is greater than the yield strength; 4) the antenna return loss is greater than the allowable value.

[0108] S2. Based on step S1, characterize and quantify the multi-source uncertainty factors of the skin conformal antenna, establish a performance simulation analysis model of the skin conformal antenna, and simulate its performance response (structural strength and electrical performance, etc.) under multi-physics coupling.

[0109] Adjusting the wing's ply angle to keep the wing's first natural frequency away from the antenna's operating frequency reduces the possibility of resonance; adding local reinforcement structures at the antenna mounting location reduces the impact of wing deformation on the antenna; optimizing the antenna's feed network improves its impedance matching stability under vibration conditions, thereby enhancing the overall performance of the wing-antenna system.

[0110] S21. Characterize and quantify the multi-source uncertainties of conformal skin antennas;

[0111] The multi-source uncertainties include: the dimensions of the conformal antenna structure, material properties, and multi-source uncertainties of the load.

[0112] Considering manufacturing errors, the layup thickness and honeycomb thickness of the single-layer composite material laminate are random uncertain design variables, the elastic modulus of the material mechanical properties is a random design parameter, and the inflow velocity, angle of attack, and temperature load are random uncertain parameters.

[0113] In this embodiment, the uncertainty attributes and their quantification (uncertainty design variables and parameters) are shown in Table 1.

[0114] Table 1

[0115]

[0116] S22. Based on the random distribution characteristics of the design parameters and variables in step S21, perform Latin hypercube sampling and simulate and analyze the performance response of the conformal antenna with composite material skin under multi-physics coupling.

[0117] The performance of the composite material skin conformal antenna under multi-physics coupling includes: the stress and strain of the skin antenna, as well as the antenna's electrical performance, radiation pattern, and gain.

[0118] As a stratified sampling technique, Latin hypercube sampling can obtain relatively accurate statistical properties with fewer sample points in computer simulations and finite element analyses, thereby reducing computational costs. This method avoids repeated sampling in the sample space, saving sampling times and time, while maximizing computational efficiency and result accuracy.

[0119] First, Latin hypercube sampling is performed. The dynamic analysis expression of the conformal antenna with composite skin under multiphysics coupling is as follows:

[0120] (2);

[0121] in, This represents the conformal antenna mass matrix of the wing skin. Indicates structural deformation. This represents the first derivative of the transformation. Represents the transformed second derivative; Represents the structural damping matrix. Represents the structural stiffness matrix. This indicates the load that the structure bears.

[0122] Then, an accurate electromagnetic model of the conformal antenna with skin is established using electromagnetic simulation software (such as HFSS). The antenna type, geometric dimensions, feeding method, layout of radiating elements, and relative positional relationship with the skin are set. The electrical performance of the antenna is analyzed, and the expression is as follows:

[0123] (3);

[0124] in, This indicates the electrical performance of the antenna. and Indicates spatial orientation. Indicates antenna structural parameters, Indicates temperature. , and Indicates the first time the array surface is subjected to external load and temperature load. line, number Positional deviation of each radiation unit Functions representing the effects of external loads and temperature loads. and This indicates the spacing between radiating elements, setting the antenna to have... One radiation unit. and They represent the first line, number The amplitude and phase of the excitation current of the column position radiation element. Represents the free space wave constant. This represents the wavelength in free space. The element radiation pattern is represented by the following expression:

[0125] (4);

[0126] in, and These represent the length and width of the rectangular radiating element, respectively. This indicates the thickness of the antenna array. Antenna electrical performance refers to the key electrical characteristic parameters exhibited by the antenna during electromagnetic wave radiation and reception, the main parameters of which include: antenna gain and return loss.

[0127] Antenna gain is the ratio of the radiated power density of an antenna in a certain direction to the radiated power density of an ideal point source antenna under the same input power, usually expressed in decibels (dB). A higher antenna gain indicates greater radiated power in its primary radiation direction, resulting in wider signal coverage. The mathematical expression is as follows:

[0128] (5);

[0129] in, Radiation efficiency refers to the proportion of input power converted into radiated power. The directivity coefficient describes the spatial concentration of energy radiated by an antenna. The expression for the directivity coefficient is as follows:

[0130] (6);

[0131] in, Indicates the antenna in direction The radiation intensity, , This represents the total radiated power of the antenna. If the far-field radiation pattern of the antenna is known... The directional coefficient is then calculated by integration, as shown in the following expression:

[0132] (7);

[0133] in, Represents the maximum directionality coefficient. Represents the solid angle of the entire sphere, and , This represents the normalized pattern function.

[0134] Return loss is a key parameter for measuring the impedance matching degree of an antenna or radio frequency system. It represents the ratio of incident power to reflected power, usually measured in decibels (dB). A higher return loss value indicates lower reflected power and better impedance matching. The expression is as follows:

[0135] (8);

[0136] in, The voltage reflection coefficient is expressed as follows:

[0137] (9);

[0138] in, This indicates the input impedance of the antenna. This represents the characteristic impedance of the transmission line.

[0139] S23. Based on the stress and strain analysis results from step S22, the fatigue life of the composite material skin structure is evaluated using the critical plane method, as shown in the following expression:

[0140] (10);

[0141] in, Indicates the range of shear strain. Indicates the range of normal strain. Indicates the structural fatigue life. Represents a constant. and These represent the fatigue strength index and the fatigue ductility index, respectively. Indicates the elastic modulus. Indicates the fatigue strength coefficient. This represents the fatigue ductility coefficient.

[0142] S3. Based on the multi-physics coupling performance analysis in step S2, establish a deep learning-based performance prediction model for the skin conformal antenna.

[0143] First, determine the deep learning network structure of the deep learning-based conformal antenna performance prediction model, such as... Figure 2 As shown, this embodiment uses a multi-layer fully connected network. The input nodes are: the thickness of the upper and lower composite plates, the thickness of the upper and lower honeycomb structures, temperature, material elastic modulus, incoming flow velocity and angle of attack. The outputs are the stress, strain, maximum deformation and antenna electrical performance of the skin critical section.

[0144] The first layer of input nodes includes: thickness of the upper and lower composite layers, thickness of the upper and lower honeycomb structures, temperature, material elastic modulus, inflow velocity, and angle of attack. express.

[0145] in, Indicates design variables, Indicates the number of design variables. Indicates design parameters, Indicates the number of design parameters. This indicates the transpose operation.

[0146] Output layer node is , These represent the maximum stress, strain, maximum deformation, and electrical performance of the conformal antenna with skin, respectively. The output of the hidden layer nodes is , Indicates the first Hidden layer The output of each node. The activation function is expressed as follows:

[0147] (11);

[0148] Then the first Hidden layer output layer nodes The input and output (the propagation relationship of the feedforward neural network) are calculated using the following expressions:

[0149] (12);

[0150] in, Indicates the first The first hidden layer One neuron, Indicates the first One output, Indicates the first One input, Indicates the number of inputs. This indicates the number of nodes in each hidden layer. Indicates the first The first hidden layer Threshold of each neuron. Indicates the first Hidden layer nodes With the Hidden layer nodes Weighting coefficients; This represents the bias term for each layer of the neural network.

[0151] Get the sum of the output values ​​of all output layers Then compare it with the corresponding true value Compare the errors of the obtained sample points, and then obtain the total errors of all training samples. Let the total number of errors be... For each sample point, the total error function The expression is as follows:

[0152] (13);

[0153] Then, gradient descent is used to correct the weights and thresholds to minimize the total error for the hidden layer. There are 1 node, and the learning rate is set to 1. The weight adjustment amount is The threshold adjustment amount is The steepest gradient descent method is used to calculate the weights of each layer. Similarly, the adjustment amount of the weights of the output layer nodes can be calculated. and threshold adjustment amount The expression is as follows:

[0154] (14);

[0155] in, Indicates the output layer activation value. This represents the adjustment amount of the output layer activation value. This represents the input value of the y-th node in the input layer. This represents the target output value of the j-th node in the output layer. This represents the weight between the i-th input node and the j-th hidden layer node. This represents the input value of the s-th node in the input layer.

[0156] Finally, the root mean square error (RMSE) and coefficient of determination were used to determine the results. The performance of a machine learning model can be evaluated using the following expression:

[0157] (15); (16);

[0158] in, Indicates the number of test samples. This represents the experimental value for each test sample. This represents the predicted value of each test sample based on the deep learning model. express The average of the test values ​​of the test samples.

[0159] S4. Based on the performance prediction model of the conformal antenna with skin established in step S3, establish an integrated optimization design model of the conformal antenna with skin under fatigue reliability constraints.

[0160] S41. Optimize the design variables, objective function, and constraint conditions;

[0161] The optimization design variables include: the layup thickness and honeycomb thickness of the single-layer composite material plate; the objective function is to maximize the gain of the antenna array. Constraints include: probabilistic fatigue life constraint of the skin structure, maximum mass constraint, return loss constraint, and maximum deformation constraint.

[0162] S42. Based on step S41, establish an integrated optimization design model for skin conformal antenna under fatigue reliability constraints.

[0163] The expression for the integrated optimization design model of the conformal antenna with skin is as follows:

[0164] (17);

[0165] in, Indicates antenna gain. Represents a vector of random design variables. Indicates random design parameters. This indicates the required fatigue life of the wing structure. Indicates minimum return loss. This indicates the allowable return loss value. This indicates the maximum deformation of the conformal antenna structure with skin. This indicates the maximum allowable deformation of the conformal antenna structure with skin. This indicates the weight of the conformal antenna structure with skin. This indicates the maximum allowable weight of the conformal antenna structure with skin.

[0166] S5. Based on step S4, solve the optimal design variables of the skin conformal antenna using an intelligent optimization algorithm, analyze the multi-physics performance of the optimized structure, verify the optimization results, and complete the skin conformal antenna optimization design under fatigue reliability constraints.

[0167] First, based on the first-order Taylor expansion method, the fatigue reliability constraint is expanded at the mean of the random design variables and random design parameters using the first-order Taylor expansion method, as shown in the following expression:

[0168] (18);

[0169] in, and These represent the mean vectors of the design variables and design parameters, respectively. Indicates the number of design variables. Indicates design variables, Indicates the number of design parameters. Indicates design parameters, This represents the mean of the design variables. This represents the average value of the design parameters.

[0170] Then, based on the augmented Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem, as shown in the following expression:

[0171] (19);

[0172] in, Describe the objective function. Indicates the output. Indicates the first The Lagrange multipliers of the next iteration, Indicates the first The penalty factor for each iteration. Indicates the first Lagrange multipliers for each inequality constraint in each iteration Indicates the first Slack variables of a constraint, Indicates the first One constraint condition. Indicates the number of constraints.

[0173] Then minimize the slack variables to transform equation (19) into one containing only design variables. and objective function The expression is as follows:

[0174] (20);

[0175] Then, the particle swarm optimization (PSO) algorithm is used to solve the unconstrained optimization design problem of equation (20), and the following conditions are set. In a 1-dimensional space, there are Q particles. Represented as ,Will Substitute into the fitness function Find the fitness value; particle speed ,particle The best position an individual has ever experienced: The best position the population has ever experienced: ,particle The The dimensional velocity update expression is as follows:

[0176] (twenty one);

[0177] in, Indicates the first Sub-iteration particles The first of the flight velocity vectors dimensional components, Indicates the first Sub-iteration particles The position vector of the first dimensional components, , Represents the acceleration constant, and adjusts the maximum learning step size. , These represent two random functions, taking values ​​in the range [0, 1], to increase the randomness of the search. Indicates inertial weight, which adjusts the search range of the solution space.

[0178] particle The The dimension component update expression is as follows:

[0179] (twenty two);

[0180] The fatigue reliability index iteration is based on the first-order second-moment method to evaluate fatigue reliability, and the expression is as follows:

[0181] (twenty three);

[0182] in, This indicates the required fatigue life. and Let represent the mean and standard deviation of fatigue life, respectively. and This represents the vector of mean values ​​of the random design variables and random design parameters. This represents the vector of the mean and optimal values ​​of random design variables. This represents the integral function of the standard normal distribution.

[0183] Finally, the optimization results were verified and confirmed by combining simulation analysis. After obtaining the optimization results of the design variables, a geometric model of the conformal antenna of the composite material wing was established. The multi-physics coupling performance was analyzed based on the finite element simulation method to obtain data such as stress, strain and maximum deformation of the critical section. Then, the antenna return loss, gain and other electrical performance were simulated and analyzed by MATLAB software to verify the optimization results.

[0184] The stress-strain results of the conformal antenna structure with skin are as follows: Figure 3 As shown, where Figure 3 (a) shows the equivalent elastic strain analysis results of the conformal antenna structure with skin. Figure 3 (b) shows the equivalent stress analysis results of the conformal antenna structure with skin. Stress-strain analysis can provide a reference for structural strength and stability. The antenna electrical performance analysis results are as follows: Figure 4 As shown, the analysis yields the antenna's gain pattern and return loss results. The gain pattern illustrates the antenna's radiation or reception capabilities in different directions, as well as the direction of maximum gain. The return loss result indicates the amount of signal reflected by the antenna; low loss implies high antenna efficiency and good signal transmission. Through finite element analysis and electrical performance analysis, optimal design parameters for electrical performance can be found while ensuring structural strength.

[0185] In summary, the method of this invention comprehensively considers the complex loads faced by composite material wings during flight, the dispersion of material properties, and the coupling effect between the wing skin structure and the antenna. It can not only analyze the deformation and vibration responses of the wing skin structure with high precision, but also reveal how these responses affect the antenna's radiation characteristics, gain, and other core electrical properties, providing a technical approach for the overall performance evaluation and optimization of the wing skin structure-antenna integrated system under multi-physics coupling environments.

[0186] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. An optimization design method for a skin-conformal antenna under fatigue reliability constraints, the specific steps of which are as follows: S1. Analyze the conformal antenna structure and service load of composite material wing skin, and identify the main failure modes of the conformal antenna. The skin antenna comprises: Upper and lower composite material layers, honeycomb structure and antenna array; Composite laminates are made of single-layer composite materials laid up at different angles. The structural optimization design takes into account the layup geometry of the single-layer materials and bears aerodynamic loads, vibration loads and temperature loads. The ply geometry includes: the thickness of each single layer, the ply direction, and the ply sequence; First, a three-dimensional finite element model of the conformal antenna of the composite wing skin is constructed based on the finite element analysis method. During the modeling process, the geometry of the wing, the layup structure, fiber direction, material properties and boundary conditions of the upper and lower composite material plates are set, and the element mesh is divided according to the actual situation. The material properties include: elastic modulus, Poisson's ratio, shear modulus, and density; To address the anisotropic properties of composite materials, a suitable material constitutive model is employed to describe their mechanical behavior. The principal directions of the material are represented by coordinates l, 2, and 3. The expressions for stress distribution and strain in the upper and lower composite laminates within coordinate system 1, 2, and 3 are as follows: （1）； in, , , , , , Represents stress components in tensor form. Represents the normal stress along the principal axes of the material. Represents shear stress; , , , , , Represents strain components in tensor form. Represents the normal strain along the principal axis of the material. Indicates shear strain; , This represents the elastic modulus of a composite material in the tensile direction. , , Indicates shear modulus, and Indicates Poisson's ratio; Finally, the main failure modes of the skin antenna were determined, including: 1) under multi-physics coupling, the deformation of the upper and lower composite material layers and the antenna array exceeds the allowable value; 2) under multi-physics coupling, the fatigue life of the upper and lower composite material layers is less than the design value; 3) static strength is greater than yield strength; 4) antenna return loss is greater than the allowable value. S2. Based on step S1, characterize and quantify the multi-source uncertainty factors of the skin conformal antenna, establish a performance simulation analysis model of the skin conformal antenna, and simulate its performance response under multi-physics coupling. S21. Characterize and quantify the multi-source uncertainties of conformal skin antennas; The multi-source uncertainty factors include: the dimensions of the conformal antenna structure, material properties, and multi-source load uncertainty. Considering manufacturing errors, the layup thickness and honeycomb thickness of the single-layer composite material laminate are random uncertain design variables, the elastic modulus of the material mechanical properties is a random design parameter, and the inflow velocity, angle of attack, and temperature load are random uncertain parameters. S22. Based on the random distribution characteristics of the design parameters and variables in step S21, perform Latin hypercube sampling and simulate and analyze the performance response of the conformal antenna with composite material skin under multi-physics coupling. The performance of the composite material skin conformal antenna under multi-physics coupling includes: the stress and strain of the skin antenna, as well as the antenna's electrical performance, radiation pattern, and gain; First, Latin hypercube sampling is performed. The dynamic analysis expression of the conformal antenna with composite skin under multiphysics coupling is as follows: （2）； in, This represents the conformal antenna mass matrix of the wing skin. Indicates structural deformation. This represents the first derivative of the transformation. Represents the transformed second derivative; Represents the structural damping matrix. Represents the structural stiffness matrix. Indicates the load borne by the structure; Then, the antenna type, geometry, feeding method, radiating element layout, and relative positional relationship with the skin are defined, and the antenna's electrical performance is analyzed, as shown in the following expression: （3）； in, This indicates the electrical performance of the antenna. and Indicates spatial orientation. Indicates antenna structural parameters, Indicates temperature. , and Indicates the first time the array surface is subjected to external load and temperature load. line, number Positional deviation of each radiating element Functions representing the effects of external loads and temperature loads. and This indicates the spacing between radiating elements, setting the antenna to have... One radiation unit; and They represent the first line, number The amplitude and phase of the excitation current of the column position radiation element; Represents the free space wave constant. Indicates the wavelength in free space; The element radiation pattern is represented by the following expression: （4）； in, and These represent the length and width of the rectangular radiating element, respectively. Indicates the thickness of the antenna array; Antenna electrical performance parameters include: antenna gain and return loss; antenna gain The expression is as follows: （5）； in, Radiation efficiency refers to the proportion of input power converted into radiated power. The directivity coefficient describes the spatial concentration of energy radiated by an antenna. The expression for the directivity coefficient is as follows: （6）； in, Indicates the antenna in direction The radiation intensity, , This represents the total radiated power of the antenna; if the far-field radiation pattern of the antenna is known... The directional coefficient is then calculated by integration, as shown in the following expression: （7）； in, Represents the maximum directionality coefficient. Represents the solid angle of the entire sphere, and , Represents the normalized pattern function; Return loss The expression is as follows: （8）； in, The voltage reflection coefficient is expressed as follows: （9）； in, This indicates the input impedance of the antenna. This represents the characteristic impedance of the transmission line; S23. Based on the stress and strain analysis results from step S22, the fatigue life of the composite material skin structure is evaluated using the critical plane method, as shown in the following expression: （10）； in, Indicates the range of shear strain. Indicates the range of normal strain. Indicates the structural fatigue life. Represents a constant. and These represent the fatigue strength index and the fatigue ductility index, respectively. Indicates the elastic modulus. Indicates the fatigue strength coefficient. Indicates the fatigue ductility coefficient; S3. Based on the multi-physics coupling performance analysis in step S2, establish a deep learning-based performance prediction model for the skin conformal antenna. First, the deep learning network structure of the deep learning-based conformal antenna performance prediction model is determined. A multi-layer fully connected network is adopted, and the input nodes of the first layer are: the thickness of the upper and lower composite plates, the thickness of the upper and lower honeycomb structures, temperature, material elastic modulus, incoming flow velocity, and angle of attack. express; in, Indicates design variables, Indicates the number of design variables. Indicates design parameters, Indicates the number of design parameters. Indicates the transpose operation; Output layer node is , These represent the maximum stress, strain, maximum deformation, and electrical performance of the conformal antenna with skin, respectively; The output of the nodes in the hidden layer is , Indicates the first Hidden layer The output of each node; The activation function is expressed as follows: （11）； Then the first Hidden layer output layer nodes The input and output calculation expressions are as follows: （12）； in, Indicates the first The first hidden layer One neuron, Indicates the first One output, Indicates the first One input, Indicates the number of inputs. This indicates the number of nodes in each hidden layer. Indicates the first The first hidden layer The threshold of each neuron; Indicates the first Hidden layer nodes With the Hidden layer nodes Weighting coefficients; This represents the bias term for each layer of the neural network; Get the sum of the output values ​​of all output layers Then compare it with the corresponding true value Compare the errors of the obtained sample points, and then obtain the total errors of all training samples. Let the total number of errors be... For each sample point, the total error function is... The expression is as follows: （13）； Then, gradient descent is used to correct the weights and thresholds to minimize the total error for the hidden layer. There are 1 node, and the learning rate is set to 1. The weight adjustment amount is The threshold adjustment amount is The steepest gradient descent method is used to calculate the weights of each layer, and the adjustment amount of the weights of the output layer nodes is calculated similarly. and threshold adjustment amount The expression is as follows: （14）； in, Indicates the output layer activation value. This represents the adjustment amount of the output layer activation value. This represents the input value of the y-th node in the input layer. This represents the target output value of the j-th node in the output layer. This represents the weight between the i-th input node and the j-th hidden layer node. This represents the input value of the s-th node in the input layer; Finally, the root mean square error (RMSE) and the coefficient of determination were used as the basis for the analysis. The performance of a machine learning model can be evaluated using the following expression: （15）； （16）； in, Indicates the number of test samples. This represents the experimental value for each test sample. This represents the predicted value of each test sample based on the deep learning model. express The average value of the test samples; S4. Based on the performance prediction model of the conformal antenna with skin established in step S3, establish an integrated optimization design model of the conformal antenna with skin under fatigue reliability constraints. Define the optimization design variables, objective function and constraints, and establish an integrated optimization design model for skin conformal antenna under fatigue reliability constraints; S5. Based on step S4, solve the optimal design variables of the skin conformal antenna using an intelligent optimization algorithm, analyze the multi-physics performance of the optimized structure, verify the optimization results, and complete the skin conformal antenna optimization design under fatigue reliability constraints.

2. The optimization design method for a skin conformal antenna under fatigue reliability constraints according to claim 1, characterized in that, Step S4 is as follows: S41. Optimize the design variables, objective function, and constraint conditions; The optimization design variables include: the layup thickness of the single-layer composite material plate and the honeycomb thickness; the objective function is to maximize the gain of the antenna array; the constraints include: fatigue reliability constraints of the skin structure, maximum mass constraints, return loss constraints, and maximum deformation constraints. S42. Based on step S41, establish an integrated optimization design model for skin conformal antenna under fatigue reliability constraints. The expression for the integrated optimization design model of the conformal antenna with skin is as follows: （17）； in, Indicates antenna gain. Represents a vector of random design variables. Represents a vector of random design parameters. This indicates the required fatigue life of the wing structure. Indicates minimum return loss. This indicates the allowable return loss value. This indicates the maximum deformation of the conformal antenna structure with skin. This indicates the maximum allowable deformation of the conformal antenna structure with skin. This indicates the weight of the conformal antenna structure with skin. This indicates the maximum allowable weight of the conformal antenna structure with skin.

3. The optimization design method for a skin conformal antenna under fatigue reliability constraints according to claim 2, characterized in that, Step S5 is as follows: First, based on the first-order Taylor expansion method, the fatigue reliability constraint is expanded at the mean of the random design variables and random design parameters using the first-order Taylor expansion method, as shown in the following expression: （18）； in, and These represent the mean vectors of the design variables and design parameters, respectively. Indicates the number of design variables. Indicates design variables, Indicates the number of design parameters. Indicates design parameters, This represents the mean of the design variables. This represents the average value of the design parameters; Then, based on the augmented Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem, as shown in the following expression: （19）； in, Describe the objective function. Indicates the output. Indicates the first The Lagrange multipliers of the next iteration, Indicates the first Next iteration penalty factor Indicates the first Lagrange multipliers for each inequality constraint in each iteration Indicates the first Slack variables of a constraint, Indicates the first One constraint condition. Indicates the number of constraints; Then minimize the slack variables to transform equation (19) into one containing only design variables. and objective function The expression is as follows: （20）； Then, the Particle Swarm Optimization (PSO) algorithm is used to solve the unconstrained optimization design problem of equation (20), and the following is set: In a 1-dimensional space, there are Q particles; particles Represented as ,Will Substitute into the fitness function Find the fitness value; particle speed ,particle The best position an individual has ever experienced: The best position the population has ever experienced: ,particle The The dimensional velocity update expression is as follows: （21）； in, Indicates the first Sub-iteration particles The first of the flight velocity vectors dimensional components, Indicates the first Sub-iteration particles The position vector of the first dimensional components, , Represents the acceleration constant. , Let [the two numbers] represent two random functions, with values ​​ranging from [0, 1]. Indicates inertia weight; particle The The dimension component update expression is as follows: （22）； The fatigue reliability index iteration is based on the first-order second-moment method to evaluate fatigue reliability, and the expression is as follows: （23）； in, This indicates the required fatigue life. and Let represent the mean and standard deviation of fatigue life, respectively. and This represents the vector of mean values ​​of the random design variables and random design parameters. This represents the vector of the mean and optimal values ​​of random design variables. Represents the integral function of the standard normal distribution; Finally, the optimization results were verified and confirmed by combining simulation analysis, the optimization results of the design variables were obtained, the geometric model of the conformal antenna of the composite material wing skin was established, and the multi-physics coupling performance was analyzed based on the finite element simulation method to obtain the stress, strain and maximum deformation data of the critical section. Then, the antenna return loss and gain electrical performance were analyzed by software simulation to verify the optimization results and complete the optimization design of the conformal antenna of the skin under fatigue reliability constraints.

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